latex-pictures

A collection of TikZ drawings and other images 🖌️
elliptic-curve-group-structure.tikz (1335B)

 1 % This picture represents the group structure of the points of an elliptic
 2 % curve
 3 \begin{tikzpicture}[yscale=.7]
 4   % The axis
 5   \draw[->] (-3,    0) -- (3.5,   0);
 6   \draw[->] ( 0, -3.2) -- (  0, 3.2);
 7 
 8   \clip(-3., -3.2) rectangle (3.5, 3.2);
 9 
10   % The curve
11   \draw[thick, smooth, samples=100, domain=-2.6712:0.5950] 
12     plot(\x, {sqrt((\x)^(3)-5.9*(\x)+3.3)});
13   \draw[thick, smooth, samples=100, domain=2.0762:3.5] 
14     plot(\x, {sqrt((\x)^(3)-5.9*(\x)+3.3)});
15   \draw[thick, smooth, samples=100, domain=-2.6712:0.5950] 
16     plot(\x, {0-sqrt((\x)^(3)-5.9*(\x)+3.3)});
17   \draw[thick, smooth, samples=100, domain=2.0762:3.5] 
18     plot(\x, {0-sqrt((\x)^(3)-5.9*(\x)+3.3)});
19 
20   % The intersection lines
21   \draw[thick, color=violet] (     -3, 1.2218) -- (    3.5, 2.5105);
22   \draw[thick, color=violet] (-2.5534,   -3.2) -- (-2.5534,    3.2);
23 
24   % The intersection points
25   \filldraw (                  0,  1.8165902124584950) circle (1.0pt);
26   \filldraw ( 2.5927223574355067,  2.3306137033629240) circle (1.0pt);
27   \filldraw (-2.5534168046838945,  1.3103592942448403) circle (1.0pt);
28   \filldraw (-2.5534168046838945, -1.3103592942526257) circle (1.0pt);
29 
30   % The labels
31   \draw ( 0,  2.2346057845515620) node[right]{$P$};
32   \draw ( 3,  2.6354835353265860) node {$Q$};
33   \draw (-2, -1.0195783099751021) node {$P+Q$};
34 \end{tikzpicture}